Matrices
Category : 10th Class
Matrices
Matrices
In this type of questions a set of numbers or letters are given in a figure which is divided into different cells. These numbers or letters form a pattern by applying some logic - either row- wise or column-wise. One cell of the matrix is left empty. The candidate is required to analyse the matrix to find out the logic applied in the pattern and select one from the given options which will complete it.
Example:
|
15 |
4 |
18 |
|
10 |
17 |
6 |
|
5 |
34 |
3 |
|
30 |
2 |
? |
(a) 4 (b) 36
(c) 38 (d) 19
Ans. (b)
Explanation: The pattern of the logic is column wise. The product of the numbers in first and second column is equal to the product of the numbers in third and fourth column
i.e. \[15~\times 10=5~\times 30,4~\times 17=34~\times 2,\text{ }18~\times 6=3\times ?\]
Thus, ? = 36
|
1 |
4 |
6 |
281 |
|
5 |
3 |
2 |
160 |
|
3 |
4 |
5 |
? |
(a) 281 (b) 160
(c) 216 (d) 370
Ans. (c)
Explanation: The logic in the pattern is as follows
\[{{1}^{3}}+{{4}^{3}}+{{6}^{3}}=1+64+216=281\]
\[{{5}^{3}}+{{3}^{3}}+{{2}^{3}}=125+27+8=160\]
So, \[{{3}^{3}}+{{4}^{3}}+{{5}^{3}}=27+64+125=216\]
3. Place the correct letter in the empty cell of the following matrix.
|
J |
M |
|
T |
X |
|
O |
L |
H |
E |
A |
(a) N (b) P
(c) M (d) Q
Ans. (d)
Explanation The pattern is as follows:
In this type of matrix columns and rows are numbered and a letter from matrices are represented first by its row and next by column. The candidate is required to identity the set for the given word.
1. Identify the set for the given word.
|
|
0 |
1 |
2 |
3 |
4 |
|
0 |
C |
A |
F |
E |
D |
|
1 |
C |
D |
A |
E |
D |
|
2 |
D |
E |
C |
F |
E |
|
3 |
A |
D |
D |
D |
C |
|
4 |
D |
C |
A |
C |
A |
Farm
|
|
5 |
6 |
7 |
8 |
9 |
|
5 |
T |
R |
R |
S |
M |
|
6 |
S |
T |
M |
R |
S |
|
7 |
R |
S |
P |
T |
P |
|
8 |
P |
S |
T |
R |
T |
|
9 |
P |
M |
P |
M |
S |
(a) 20, 31, 76, 68 (b) 02, 30, 85, 65
(c) 23, 12, 68, 96 (d) 44, 43, 87, 57
Ans. (c)
Explanation: F is represented by row 2, column 3
A by row 1, column 2
R by row 6, column 8
M by row 9, column 6
2. Identify the set for the given word.
|
|
0 |
1 |
2 |
3 |
4 |
|
0 |
C |
D |
F |
H |
A |
|
1 |
H |
A |
D |
F |
C |
|
2 |
C |
F |
B |
H |
A |
|
3 |
A |
A |
F |
H |
B |
|
4 |
B |
C |
F |
D |
H |
Fish
|
|
5 |
6 |
7 |
8 |
9 |
|
5 |
P |
I |
Q |
R |
S |
|
6 |
Q |
R |
I |
P |
S |
|
7 |
S |
Q |
I |
P |
P |
|
8 |
S |
P |
R |
Q |
I |
|
9 |
I |
S |
P |
R |
Q |
(a) 13, 67, 96, 44 (b) 02, 56, 76, 23
(c) 66, 67, 75, 33 (d) 21, 56, 85, 32
Ans. (a)
F is represented by row 1, column 3
I by row 6, column 7
S by row 9, column 6
H by row 4, column 4
Snap Test
Direction (Question 1 to 5): In each question given below replace the question mark from the matrix with the correct number.
1.
|
4 |
5 |
6 |
5 |
|
6 |
7 |
8 |
21 |
|
3 |
7 |
7 |
9 |
|
5 |
7 |
? |
10 |
(a) 8 (b) 6
(c) 9 (d) 10
Ans. (a)
Explanation: The pattern is as follows:
\[{{4}^{2}}+{{5}^{2}}-{{6}^{2}}=16+25-36=5\]
\[{{6}^{2}}+{{7}^{2}}-{{8}^{2}}=36+49-64=21\]
\[{{3}^{2}}+{{7}^{2}}-{{7}^{2}}=9+49-49=9\]
2.
|
4 |
5 |
7 |
7 |
|
5 |
6 |
3 |
13 |
|
7 |
4 |
5 |
13 |
|
6 |
4 |
8 |
? |
(a) 10 (b) 12
(c) 14 (d) 16
Ans. (b)
Explanation: The pattern is as follows:
\[4\times ~5+7=27-20=7\]
\[5\times ~6+3=33-20=13\]
\[7\times ~4+5=33-20=13\]
3.
|
5 |
4 |
3 |
22 |
|
6 |
? |
4 |
26 |
|
5 |
7 |
3 |
28 |
(a) 2 (b) 3
(c) 4 (d) 5
Ans. (c)
Explanation: The pattern is as follows:
\[5\times 1+4\times ~2+3~\times 3=5+8+9=22\]
\[5\times ~1+7~\times 2+3~\times 3=5+14+9=28\]
4.
|
7 |
9 |
3 |
21 |
|
8 |
6 |
4 |
12 |
|
12 |
6 |
? |
8 |
(a) 7 (b) 8
(c) 9 (d) 6
Ans. (c)
Explanation: The pattern is as follows:
\[(7\times ~9)~\div 3=21\]
\[(8~\times 6)~\div 4=12\]
5.
|
6 |
4 |
5 |
5 |
|
7 |
8 |
9 |
8 |
|
12 |
12 |
9 |
? |
(a) 7 (c) 11
(c) 9 (d) 6
Ans. (b)
Explanation: The pattern is as follows
\[\left( 6+4+5 \right)~\div 3=5\]
\[\left( 7+8+9 \right)~\div 3=8\]
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